Methods and apparatus to model consumer choice sourcing

ABSTRACT

Methods and apparatus are disclosed to model consumer choices. An example method includes adding, with a processor, a set of products having respondent choice data to a base multinomial logit (MNL) model, the base MNL model including an item utility parameter and a price utility parameter associated with corresponding ones of products in the set of products, generating, with the processor, a number of copies of the base MNL model to form an aggregate model based on a number of the corresponding ones of products in the set of products, each one of the number of copies of the base MNL model exhibiting an effect of an independence of irrelevant alternatives (IIA) property, proportionally affecting interrelationships, with the processor, between dissimilar ones of the number of products in the set by inserting sourcing effect values in the aggregate model to be subtracted from respective ones of the item utility parameters, estimating, with the processor, the item utility parameters of the aggregate model based on the number of copies of the base MNL model and the respondent choice data, and calculating, with the processor, the choice probability for the corresponding ones of the products in the set of products based on the estimated item utility parameters and the price utility parameters.

RELATED APPLICATION(S)

This patent arises from a continuation of U.S. patent application Ser.No. 13/081,924, which is entitled “METHODS AND APPARATUS TO MODELCONSUMER CHOICE SOURCING” and which was filed on Apr. 7, 2011. U.S.patent application Ser. No. 13/081,924 is hereby incorporated byreference in its entirety.

FIELD OF THE DISCLOSURE

This disclosure relates generally to market research and, moreparticularly, to methods and apparatus to model consumer choicesourcing.

BACKGROUND

Choice modeling techniques allow market researchers to assess consumerbehavior based on one or more stimuli. Consumer preference data iscollected during the one or more stimuli, such as a virtual shoppingtrip in which consumers are presented with any number of selectableproducts (e.g., presented via a kiosk, computer screen, slides, etc.).The consumer preferences associated with products may be referred to asutilities, which may be the result of one or more attributes of theproduct. While choice modeling allows market researchers to predict howone or more consumers will respond to the stimuli, such analysistechniques typically assume that each item in a virtual shopping trip isequally substitutable relative to all other items available to theconsumer.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of an example system to modelconsumer choice sourcing.

FIG. 2 is a schematic illustration of an example aggregate logitsourcing engine of the example system of FIG. 1.

FIG. 3 is an example multinomial logit model generated by the exampleaggregate logit sourcing engine of FIGS. 1 and 2.

FIG. 4 is a portion of an example aggregate model structure generated bythe example aggregate logit sourcing engine of FIGS. 1 and 2.

FIG. 5 is a portion of an example matrix infused aggregate modelstructure generated by the example aggregate logit sourcing engine ofFIGS. 1 and 2.

FIG. 6 is a portion of an example geometric matrix generated by theexample aggregate logit sourcing engine of FIGS. 1 and 2.

FIGS. 7-9 are flowcharts representative of example machine readableinstructions that may be executed to implement the example system shownin FIGS. 1 and 2.

FIG. 10 is a schematic illustration of an example processor platformthat may execute the instructions of FIGS. 7-9 to implement any or allof the example methods, systems, and apparatus described herein.

DETAILED DESCRIPTION

Methods and apparatus are disclosed to model consumer choices. Anexample method includes identifying a set of products, receivingrespondent choice data associated with the set of products, and addingthe set of products to a base multinomial logit (MNL) model. The examplemethod also includes generating, with a programmed processor, a numberof copies of the MNL model to form an aggregate model based on a numberof products in the set, each copy including an item utility parameterfor each product in the set of products, and creating a matrix structurebased on the number of products in the set, the matrix structure to besubtracted from each item utility parameter in the aggregate model.Further, the example method includes estimating each item utilityparameter of the aggregate model and the matrix structure based on thenumber of copies of the MNL model and the respondent choice data, andcalculating a choice probability based on each of the estimated utilityparameters.

Market researchers, product promoters, marketing employees, agents,analysts, and/or other people and/or organizations chartered with theresponsibility of product management (hereinafter collectively referredto as “analysts”) typically attempt to justify informal and/orinfluential marketing decisions using one or more techniques thatpredict sales of one or more products of interest. Accurate forecastingmodels are useful to facilitate these decisions. In some circumstances,a product may be evaluated by one or more researchpanelists/respondents, which are generally selected based upontechniques having a statistically significant confidence level that suchrespondents accurately reflect a given demographic of interest.Techniques to allow respondents to evaluate a product, which allows theanalysts to collect valuable choice data, include focus groups and/orpurchasing simulations that allow the respondents to view and evaluateproduct concepts (e.g., providing images of products on a monitor,asking respondents whether they would purchase the products, discretechoice exercises, etc.).

The methods and apparatus described herein include, in part, one or moremodeling techniques to facilitate sales forecasting and allow analyststo make informed marketing decisions. The modeling techniques describedherein may operate with one or more modeling techniques, consumerbehavior modeling, and/or choice modeling.

Generally speaking, choice modeling is a method to model a decisionprocess of an individual in a particular context. Choice models maypredict how individuals will react in different situations (e.g., whathappens to demand for product A when the price of product Bincreases/decreases?). Predictions with choice models may be made overlarge numbers of scenarios and are based on the concept that peoplechoose between available alternatives in view of one or more attributesof the products (e.g., price, size, tradedress, feature(s), etc.). Forexample, when presented with a choice to take a car or bus to get towork, each of the alternative choices may be separated into threeexample attributes: price, time and convenience. For each attribute, arange of possible levels may be defined, such as three levels of price(e.g., $0.50, $1.00 or $1.50), two levels of time (e.g., 5 minutes or 20minutes, corresponding to two attributes of “convenient” or“not-convenient,” respectively). In the event a transportation modeexists that is cheapest, takes the least amount of time and is mostconvenient, then that transportation mode is likely to be selected.However, tradeoffs exist that cause a consumer to make choices, in whichsome consumers place greater weight on some attributes over others. Forsome consumers, convenience is so important that price has little effecton the choice, while other consumers are strongly motivated by price andwill endure greater inconvenience to acquire the lowest price.

In the context of store, retail, and/or wholesale purchases, analystsmay wish to model how a consumer chooses among the products available.Alternatives may be decomposed into attributes including, but notlimited to product price, product display, or a temporary pricereduction (TPR), such as an in-store marketing promotion that prices theproduct lower than its base price. Although the methods and apparatusdescribed herein include price, display and/or TPR, any other attributesmay be considered, without limitation. Additional or alternativeattributes may include brand or variety. When making a purchasedecision, consumers balance the attributes (attribute utilities), suchas brand preferences balanced with the price and their attraction fordisplays and/or TPRs, thereby choosing the product that maximizes theiroverall preference.

Although choice modeling techniques offer analysts an opportunity toemploy a multinomial logit (MNL) model to predict probabilities ofdifferent consumer purchasing behaviors, use of the MNL model requiresanalyst discretion when selecting candidate available products fromwhich a customer may choose. As used herein, the term “sourcing” refersto a degree of product differentiation within a set of availableproducts from which a consumer may choose. For example, the MNL modelassumes that any choices a customer may select within a set of productsare equally substitutable for each other, which is sometimes referred toas fair share sourcing. In circumstances where the list of availableproducts includes similar products, such as a choice between Coke®,Pepsi® and RC Cola®, the degree of substitutability may be relativelyhigh. That is, in the event the original list of available cola productsremoved RC Cola® as an available selection for the consumer, then theremaining available products (i.e., Coke® and Pepsi®) are likelyconsidered realistic substitutes for each other based on, for example,comparison(s) to observed respondent behavior(s).

In other examples, if the analyst desires to study a group of productsin which one or more of the available products is not a suitablesubstitute, then the MNL model exhibits output error when calculatingand/or otherwise predicting probabilities of different consumerpurchasing behaviors. For instance, if the analyst arranges a set ofavailable products to include Coke®, Pepsi® and Sprite®, then the MNLmodel assumes that each of those available products is deemed to beequally substitutable for the other product in the event that one ormore of the selection choices become unavailable. If Pepsi® were removedfrom the list of available choices, then the MNL model calculates theprobability of remaining choice selection as though Coke® and Sprite®were equally substitutable for each other and/or otherwise preferred bythe consumer. This inherent limitation of the MNL model is sometimesreferred to as an independence of irrelevant alternatives (IIA)property, in which the MNL model treats all product sourcing as fairshare (equal) sourcing where all sourcing (e.g., any product) is equallysubstitutable to any other available product(s) under consideration.

Efforts to minimize the negative effects of the IIA property includeimplementing variants to the MNL model and/or logit models in general.Example variants include a probit (multinomial probit) model and/or anested logit model. These variants do not exhibit the negative effectsof the IIA property. However, while the nested logit does not suffer thenegative effects of the IIA property, such models require analystdiscretion when forming one or more groups of available products understudy. In other words, the MNL model and the nested logit model cannotmodel complex sourcing scenarios that may reflect real-world productavailability combinations that consumers experience. For situations inwhich the analyst wishes to identify respondent behaviors for a wholecategory of products (e.g., beverages), a realistic product mix may notbe possible when the products of a set of products cannot be consideredvalid substitutes for each other. Additionally, while the multinomialprobit model may handle complex sourcing scenarios, the multinomialprobit model does not apply a closed-form formula to calculate choiceprobabilities, thereby requiring substantial numerical integration andtime. For example, multinomial probit models having more than ten (10)to fifteen (15) parameters (e.g., products of interest to study) couldrequire days or weeks of computation time.

The methods and apparatus disclosed herein permit an analyst to considercomplex sourcing product arrangements to calculate choice probabilitiesusing a closed-form approach. At least one benefit of the methods andapparatus described herein includes realization of a computationalefficiency improvement on one or more computing resources used tocalculate choice probabilities using respondent choice data.

FIG. 1 is a schematic illustration of a system 100 to model consumerchoice sourcing. In the illustrated example of FIG. 1, the system 100includes a respondent database 102, a product selection database 104 andprice/availability control 106, each of which are inputs to an aggregatelogit sourcing (ALS) engine 108. In operation, the example ALS engine108 calculates one or more choice probabilities 110 based on choiceexercise data from the respondent database 102. Additionally, the one ormore of the choice probabilities 110 calculated by the ALS engine 108may be tailored in connection with one or more simulated price pointsand availability variations identified with the exampleprice/availability control 106.

FIG. 2 is a schematic illustration of the example ALS engine 108 ofFIG. 1. In the illustrated example of FIG. 2, the ALS engine 108includes a choice modeling engine 202, a multinomial logit (MNL) engine204, an aggregate building engine 206 and a sourcing modifier 208. Theexample sourcing modifier 208 includes a matrix engine 210, a matrixsymmetry engine 212 and a matrix spatial engine 214. In operation, oneor more models generated by the aggregate building engine 206 employdata from one or more choice modeling exercises during a modelingestimation performed by an example estimator 215 to calculate modelparameters. The calculated model parameters from the one or moregenerated models are compared to the data from the choice modelingengine 202 by a measure of fit engine 216 to determine how well theparameters fit the choice data. In some examples, the measure of fitengine 216 employs a likelihood ratio test, but other types oftechniques may be employed to determine whether the model parameters fitwith the choice data. As described in further detail below, if theexample measure of fit engine 216 determines that the model parametersdo not fit the choice data, then the example sourcing modifier 208 mayemploy one or more alternate matrix structure(s) to calculate parameteroffset value(s).

Calculated model parameters that result in an acceptable measure of fitindicate that the one or more models developed by the aggregate engine206 may be used for one or more market simulation(s). Marketsimulation(s) may be calculated by a simulation engine 218, which usesone or more product specific price points and product availabilitymeasures from the price/availability control 106 to generate the choiceprobabilities 110. For example, an analyst may establish a first pricepoint for each of the products Coke®, Pepsi® and Sprite® to allow theexample simulation engine 218 to calculate choice probabilities for eachof those products of interest. Additionally, the analyst may change oneor more price points to a second price point (e.g., make Coke® moreexpensive) to observe how the choice probabilities are affected.

Unlike one or more other models and/or modeling techniques employed tocalculate choice probabilities, the example ALS engine 108 generates amodel having a closed form. Closed form models perform significantlyfaster when compared to iterative modeling approaches, such as amultinomial probit model that can require days or weeks of computationtime when a relatively small number of products (e.g., ten) of interestis studied. Additionally, the systems, methods, apparatus and/orarticles of manufacture disclosed herein minimize the negative effectsof the IIA property when calculating choice probability values forgroups of products that may not be deemed substitutable to each other,but that may be a realistic product mix that a consumer would experiencewhen shopping. While the MNL model suffers negative effects of the IIAproperty, the aggregate modeling approach disclosed herein generates anumber of sub-models to form an aggregate model. Each sub-model, alone,is bound by the IIA property. However, each of the sub-models isassociated with a matrix structure having an offset value to representcomplex and diversified sourcing possibilities so that the aggregate sumof the sub-models is unaffected by the IIA property.

In operation, the example choice modeling engine 202 receivesinformation related to an assortment of products that is to be studiedfrom the example product selection data (database) 104. Generallyspeaking, respondents that participate in one or more choice modelingexercises are presented with any number of selectable products (e.g.,presented via a kiosk, computer screen, slides, etc.). A number ofproducts are shown multiple times to each respondent, in which one ormore attributes of the products may change during each instance ofviewing. Each virtual shopping trip displays a virtual shelf with arange of products that are organized in a manner to reflect what therespondent would see if at a retail store, for example. The choices madeby the respondents during the virtual shopping trips are stored in therespondent database 102. Unlike virtual shopping trips conducted whenemploying the MNL model, the example ALS engine 108 avoids the need tocapture analyst subjective input regarding opinions of which productsare deemed proper substitutes for each other for placement on thevirtual shelf. Reliance upon analyst discretion places limitations onstatistical repeatability, accuracy and legitimacy of the productsand/or subcategories chosen by the analyst.

Instead, the systems, methods, apparatus and/or articles of manufacturedisclosed herein allow one or more subsets of the selectable products tobe presented on the virtual shelf, in which the subsets are tailored tobe displayed in a manner that addresses one or more questions by theclient and/or analyst. For instance, a client may be interested in thechoice probabilities of RC Cola® when placed near other available colaproducts. On the other hand, the client may be interested in the choiceprobabilities of RC Cola® when placed near other soft drinks in general,and/or when placed near energy drinks. In still other examples, virtualshopping trips prompt respondents to select from a range of productsfrom one or more categories (e.g., dental products, baby food products,hair care products, laundry products, etc.) to determine choiceprobability values for the products within that category.

After the example choice modeling engine 202 obtains choice data fromthe respondents in view of the selection of products used in the virtualshopping trip(s), the choice data is stored in the example respondentdatabase 102. The example MNL engine 204 builds an MNL model having astructure based on the number of items used in the choice modelingexercise (virtual shopping trip). Typically, to prevent respondentfatigue during the choice modeling exercise, the number of products fortheir consideration is limited to eighty (80), but any other number ofproducts may be used with the example systems, methods, apparatus and/orarticles of manufacture disclosed herein.

FIG. 3 is a portion of an example MNL model structure 300 that may begenerated by the example MNL engine 204. In the illustrated example ofFIG. 3, the MNL model structure 300 represents a number of items equalto a corresponding number of products to be evaluated, which isindicated by the variable I. Each item (I) of the MNL model structure300 may include any number of corresponding parameters (β), such as itemutilities (β_(I)) (e.g., intercepts) and price utilities (β_(P)) (e.g.,slopes). As used herein, a utility represents a preference magnitude inwhich a higher utility corresponds to a higher preference. Utilityvalues may represent a general preference for a product, or mayrepresent a preference for a specific product from a specificrespondent. Without limitation, utilities may indicate a preference inview of one or more product attributes and/or price. For instance, aprice utility may increase when the price for a product decreases. Inanother example, the price utility for a product may increase when theprice of a competing product increases.

A closed-form of the MNL model structure 300 may be represented byexample Equation 1.

$\begin{matrix}{C_{i} = {\frac{^{\lbrack{\beta_{i} + {\beta_{pi}\$}}\rbrack}}{\sum\limits_{j}^{\;}^{\lbrack{\beta_{j} + {\beta_{pj}\$_{j}}}\rbrack}}.}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

In the illustrated example of Equation 1, C_(i) represents the choiceprobability for the i^(th) item (I), β_(i) represents an item utilityfor the i^(th) item (I), β_(pi) represents a price utility for thei^(th) item (I), $ represents a price of an item, and j represents theset of all items for the MNL model. Expressions of price may occurand/or otherwise be represented in any manner including, but not limitedto a retail price, a base price, a geographical price average, an indexto a base price, a logarithm of the price index, etc. As describedabove, although MNL modeling facilitates the calculation of choiceprobabilities with a closed-loop formula, thereby simplifyingcalculation efforts, the MNL model typically employs a set of productsof interest that are deemed substitutable for each other due to thepotential negative effects of the IIA property. Such limitationsinherent in the MNL model hamper efforts to study complex sourcingpatterns that may be exhibited and/or experienced by consumers whenshopping. In other words, a consumer is not typically exposed to a setof equally substitutable products on a store shelf when shopping,rather, the consumer is typically presented with substantially morevariety when reviewing one or more retail shelves.

FIG. 4 is a portion of an example aggregate model structure 400 that maybe generated by the example aggregate building engine 206. In theillustrated example of FIG. 4, the aggregate building engine 206generates a number of copies of the MNL model structure 300 based on thenumber of items (I) (i.e., products of interest) to minimize the effectsof the IIA property and allow an analyst to study a set of products thatmay not necessarily be deemed similar to each other. Each copy of theMNL model structure 300 generated by the example aggregate buildingengine 206 is a sub-model. The number of sub-models is based on thenumber of items (I), thereby generating I rows, and each row includes Iparameters (β_(X)) (e.g., utilities). The sub-models generated by theexample aggregate building engine 206 are identical to each other,except for a weighting parameter W associated with each sub-model. Eachweighting parameter W may be calculated in a manner consistent withexample Equation 2.

$\begin{matrix}{W_{S} = {\frac{^{\beta_{S}}}{\sum\limits_{j}^{\;}^{\beta_{j}}}.}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

In the illustrated example of Equation 2, S represents an indication ofeach row (sub-model) of the aggregate model structure 400 of FIG. 4,β_(S) represents a parameter associated with the S^(th) sub-model, andthe denominator of example Equation 2 represents the sum ofexponentiated parameters for the aggregate model structure 400 of FIG.4. Choice probability values for each item (i) of the set of items (I)may be calculated in a manner consistent with example Equation 3.

$\begin{matrix}{C_{i} = {\sum\limits_{S}^{\;}{W_{S}{\frac{^{\lbrack{\beta_{i} + {\beta_{pi}\$_{i}}}\rbrack}}{\sum\limits_{j}^{\;}^{\lbrack{\beta_{j} + {\beta_{pj}\$_{j}}}\rbrack}}.}}}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

The example sourcing modifier 208 builds upon the example aggregatemodel structure 400 of FIG. 4 by generating a matrix structure thatidentifies and/or otherwise calculates a parameter offset value for oneor more of the parameters (β_(X)), which is shown in FIG. 5 as a portionof an example matrix infused aggregate model structure 500. In theillustrated example of FIG. 5, the aggregate building engine 206generates matrix placeholders and incorporates them into each sub-model(rows S₁, S₂, . . . , S₁). Each matrix placeholder (M_(1,1)) includes amatrix location coordinate and may be used to identify a matrix valuefrom the example sourcing modifier 208. In operation, the matrixplaceholders (M_(1,1)) facilitate a manner in which one or more sourcingscenarios can be incorporated into the aggregate model structure 400 andto allow the analyst to study a greater variety of products of interest(e.g., the choice share effects between products when prices and/oravailability values change). In other words, the matrix placeholders(M_(1,1)) allow the aggregate model structure 400 to consider theeffects of all products of interest on a first one of those products bysubtracting a representation of sourcing effects from the preferenceparameter of the first product. For example, if the first product ofinterest is Coke® and the products of interest include other softdrinks, such as Pepsi® and Sprite®, then a sourcing effect from Pepsi®has a greater relative impact on Coke® than a sourcing effect fromSprite®. In other words, changes in availability and price for Pepsi®will have a greater effect on the choice probability associated withCoke®, but changes in availability and price for Sprite® will have alesser effect on the choice probability associated with Coke®.

The representations of sourcing effects for each of the products ofinterest (i.e., the set of items I) are generated by the example matrixengine 210. In operation, the example matrix engine 210 generates and/orotherwise forms a matrix having dimensions of (I×I), with each cellwithin the I×I matrix having a parameter value to represent a sourcingeffect for an item (i) within the set of items (I). For example, if theset of items I includes eighty (80) products to be studied by theanalyst and/or otherwise requested by a client, then the example matrixengine 210 generates a matrix that is eighty columns by eighty rows(80×80). The example I×I matrix generated by the matrix engine 210provides a manner of aggregation of sub-model sourcing adjustments sothat the IIA property does not bias resulting choice probabilitycalculations when analysts and/or clients select diverse product sets.

An example I×I matrix may be referred to as a straight matrix in whicheach matrix element corresponds to an intersection of two products fromthe set (I). However, the matrix diagonal will always include a value ofzero because the diagonal reflects a comparison between a product anditself. The intersection of each non-diagonal row and column representstwo products and reflects a degree of similarity between those twoproducts. Values for each matrix element may be constrained in a mannerconsistent with example Equations 4 and 5.

M_(S,S)=0   Equation 4.

(M _(S,Y)≧0 (S≠V)   Equation 5.

In the illustrated example of Equation 4, diagonal elements are zero,which reflects matrix cells where the row and column represent the sameproduct. In the illustrated example of Equation 5, all non-diagonalmatrix elements are constrained to positive values greater than or equalto zero. Matrix placeholders are inserted into the aggregate modelstructure 500 after each item utility parameter. Each matrix placeholderincludes a coordinate that is mapped to the aggregate model structure500 based on matching matrix rows to structure 500 rows (e.g., S values)and matching matrix columns to structure 500 columns (e.g., V values).

Considering an example choice modeling exercise that includes Coke® softdrinks, Pepsi® soft drinks and Sprite® soft drinks, the illustratedexample matrix infused aggregate model structure 500 may reveal a firstitem (row S₁) with Coke®, a second item (row S₂) with Pepsi®, and athird item (row S₃) with Sprite®. Additionally, corresponding parametersdenoted with “1,” “2,” and “3” reflect Coke®, Pepsi® and Sprite®products, respectively. In view of the instant example, parameters β₁,β₂ and β₃ refer to an indication of the preference that the respondentpool has for the corresponding brands of soft drink. From a substitutionpoint of view, assume that the choice selections from the respondentdatabase 102 identify that Coke® and Pepsi® are more substitutable foreach other, while Sprite® is not deemed a common and/or otherwiseobserved substitute for the products of Coke® and Pepsi®. As such, ifthe price of Coke® increases, then a corresponding choice probabilitythat Pepsi® will be purchased to a greater degree will increase. On theother hand, price and/or availability fluctuations of Sprite® havesubstantially less effect on the products Coke® and/or Pepsi®.

Matrix index value M_((1,1)) reflects a preference of Coke* on itself,which is constrained by example Equation 4 to equal zero. Accordingly,the example matrix infused aggregate model structure 500 does not modifythe sourcing behavior from β₁ in row S₁ (see row S₁, column V₁ of theexample matrix infused aggregate model structure 500). On the otherhand, matrix index value M_((1,2)) reflects a relative degree ofsimilarity between Coke® and Pepsi®, and matrix index value M_((1,3))reflects a relative degree of similarity between Coke® and Sprite®. Thevalue for index value M_((1,2)), based on the example assumptions thatCoke® and Pepsi® are deemed significantly more substitutable for eachother as compared to Coke® and Sprite® and/or Pepsi® and Sprite®, willbe relatively low (e.g., values closer to zero are indicative to agreater degree of similarity). That is, the sourcing effects of thepreference of Pepsi® (β₂) are significantly affected by price and/oravailability metrics associated with Coke®, as shown by the subtractionof the sourcing modifier indicative of the Coke®/Pepsi® matrixintersection (M_((1,2))) from the preference parameter associated withPepsi® (β₂) (see row S₁, column V₂ of the example matrix infusedaggregate model structure 500).

On the other hand, matrix index value M_((1,3)) is relatively highbecause it reflects a relative degree of similarity (or lack thereof)between Coke® and Sprite®. The effects of the relationship between Coke®and Sprite® are evident in the example matrix infused aggregate modelstructure 500 in row S₁, column V₃ where the relatively high value forthe sourcing modifier indicative of the Coke /Sprite matrix intersection(M_((1,3))) is subtracted from the preference parameter associated withSprite® (β₃). In the event that a price and/or availability metric forCoke® changes, the effect on Sprite® will have a lower impact on theresulting choice probability. Unlike a traditional MNL model, in whichall products under consideration are treated as equal substitutes foreach other, the example methods, apparatus, systems and/or articles ofmanufacture disclosed herein apply a matrix placeholder (M_((1,1)))having a corresponding offset value to proportionally affect choiceprobability calculations in a manner consistent with actual marketand/or customer experiences.

Values for each of the matrix cells, and values for each of theparameters of the matrix infused aggregate model structure 500 (e.g.,β₁, β_(P1), β₂, β_(P2), etc.) are calculated by iteratively estimatingthe matrix infused aggregate model structure 500 with the choice datastored in the example respondent database 102. As disclosed above, therespondent database 102 stores choice selections from respondents duringa choice modeling exercise, in which the respondents engage in virtualshopping trips where the set of items (I) (products) are presented viavirtual shelves. Initial values for each of the matrix cells and/orparameters may be set at random, predetermined values, or set via arandom number generator, in which the estimation process allows thematrix cell values and parameters to converge. After the estimationprocess completes, in which the matrix cell values and parametersconverge, the choice probability may be calculated via a closed-formapproach in a manner consistent with example Equation 6.

$\begin{matrix}{C_{i} = {\sum\limits_{S}^{\;}{W_{S}{\frac{^{\lbrack{\beta_{i} - M_{s,i} + {\beta_{pi}\$_{i}}}\rbrack}}{\sum\limits_{j}^{\;}^{\lbrack{\beta_{j} - M_{s,j} + {\beta_{pj}\$_{j}}}\rbrack}}.}}}} & {{Equation}\mspace{14mu} 6}\end{matrix}$

In some examples, the parameters associated with price (priceutilities/preferences) may be modified to facilitate scaling and addresssub-model sensitivity. For example, each price utility (e.g., β_(p1))may include a scaling price parameter (β_(p′1), β_(p′2), β_(p′3), . . ., β_(p′s)) for each row of the example matrix infused aggregate modelstructure 500. The choice probability may be calculated via aclosed-form approach in a manner consistent with example Equation 7.

$\begin{matrix}{C_{i} = {\sum\limits_{S}^{\;}{W_{S}{\frac{^{\lbrack{\beta_{i} - M_{s,i} + {{({\beta_{pi} + \beta_{p^{\prime}s}})}\$_{i}}}\rbrack}}{\sum\limits_{j}^{\;}^{{{\lbrack{\beta_{j} - M_{s,j} + \beta_{pj} + \beta_{p^{\prime}s}})}\$_{j}}\rbrack}}.}}}} & {{Equation}\mspace{14mu} 7}\end{matrix}$

As described above, the example estimator 215 performs an iterativeestimation using the model and data collected from the respondent choiceexercise. Generally speaking, values of the parameters of the examplemodel, such as the model represented by the closed-form choiceprobability of example Equation 7 and/or the example matrix infusedaggregate model structure 500, are estimated based on measured and/orempirical data. The example estimator 215 may employ one or moreestimation methods including, but not limited to a maximum likelihoodmethod, a Bayes estimation method and/or a minimum mean squared error.To ascertain whether any number of estimation iterations converge toacceptable parameter values, the example measure of fit engine 216employs a fitting test (e.g., a likelihood ratio test, etc.) todetermine how well the choice data fits with the converged parameters ofthe model (e.g., the example matrix infused aggregate model structure500). In the event that the model parameters converge, but do not fitthe choice data to an acceptable degree, the example measure of fitengine 216 employs the example sourcing modifier 208 to apply one ormore alternate matrix structures to calculate the parameter offsetvalue(s) (e.g., M_((1,1))). In other examples, the measure of fit engine216 employs one or more fitting tests during each iteration. In theevent that successive iterations do not improve by a threshold amount,then current parameter values may be accepted as final. However, in theevent that successive iterations that continue to illustrate improvementbeyond a threshold value, then the one or more iterations may continueto develop parameter value(s).

As described above, the matrix structure is based on the number ofproduct of interest (items) to be studied. The methods, apparatus,systems and/or articles of manufacture disclosed herein generate one ormore matrix structures to reflect effects of sourcing behaviors on allproducts of interest under consideration. Sourcing behaviors, which arefacilitated by matrix cell values (parameters), are subtracted from eachproduct utility in a manner that is proportional to a degree ofsimilarity between one or more other products. A straight matrix isgenerated by the example matrix engine 210 by assigning an equal numberof matrix rows and columns to form a square I×I matrix. For example, ifeighty (80) products of interest are selected for the choice modelingexercise, then the example matrix engine 210 generates an 80×80 squarematrix and populates each matrix cell at a matrix placeholder M_((1,1))having a parameter and a parameter value. Each row of the straightmatrix represents one of the eighty (80) items, and each columnrepresents the same set of eighty (80) items in the same order. In otherexamples, a matrix is formed in connection with one or moresubcategories, as described in further detail below. The diagonal of thematrix reflects intersections of the product with itself, and is set tozero. However, each off-diagonal placeholder represents an intersectionindicative of a relationship between one product and another product(e.g., a degree of similarity). During the model estimation, the exampleestimator 215 iteratively estimates both the model parameters and theparameters of the straight matrix so that each parameter converges to avalue. Initial values for all model and/or matrix parameters may beinitially set at a random number, zero and/or any other value beforeconverging during estimation in view of the choice model data stored inthe respondent database 102.

In some examples, the straight matrix may not be computationallyefficient for the ALS engine 108. The example straight matrix includes arelatively high degree of flexibility when compared to one or morealternate matrix structures, such as a symmetric matrix and/or ageometric matrix. As described in further detail below, while thesymmetric matrix and/or the geometric matrix impose a greater degree ofcomputational constraint when compared to the straight matrix, thesymmetric matrix and/or the geometric matrix may be appropriate whenmodel estimation overfits the choice model data stored in the examplerespondent database 102. For example, although the straight matrixincludes a parameter value for each and every product combination ofinterest, thereby having the greatest potential to fit the choice dataaccurately, the relatively large number of parameters may becomecomputationally intensive and fail to produce statistically relevantconvergence during each estimation iteration.

A symmetric matrix decreases the number of parameters by a factor oftwo, thereby reducing computational loads for the example estimator 215.The example matrix symmetry engine 212 forces a symmetry structure ofthe straight matrix so that each parameter value on a lower half of thediagonal is the same (e.g., linked) as each corresponding parametervalue on an upper half of the diagonal. A straight matrix may beconverted into a symmetric matrix by linking cells above the matrixdiagonal with cells below the matrix diagonal. In some examples, theanalyst and/or client may begin with a matrix structure having a morerigid form when compared to the straight matrix and, depending on ameasure of fit indication from the example measure of fit engine 216,adjust the matrix structure accordingly. In some circumstances, asymmetric matrix produces statistically appropriate measure of fitvalues to justify using the symmetric matrix. In other circumstances,the symmetric matrix fails to cause statistically appropriate measuresof fit, in which case the straight matrix may be employed.

A geometric matrix introduces a degree of structure greater than that ofthe symmetric matrix, thereby affording greater conservation ofcomputing resources during estimation by the example estimator 215.Matrix values within the geometric matrix have a spatial relationship toeach other based on a number of matrix dimensions. For ease ofdiscussion, the example geometric matrix will be described in connectionwith three (3) dimensions, but any other number of dimensions may beemployed with the example systems, methods, apparatus and/or articles ofmanufacture disclosed herein.

FIG. 6 is a portion of an example geometric matrix 600 generated by theexample matrix spatial engine 214. In the illustrated example of FIG. 6,the geometric matrix 600 includes a number of dimensions (n) (602)(columns) and a total number of items (I) (604) (rows). The number ofdimensions n is constrained to be less than or equal to the number ofitems I. Matrix values are designated by χ_((1,n)), and particular items(s) within the total number of items (I) are located in n-dimensionalspace in a manner consistent with example Equation 8.

(χ_(s,1), χ_(s,2), . . . , χ_(s,n))   Equation 8.

For example, χ_((1,1)) represents a first dimensional coordinate (e.g.,an x-axis spatial value) for a first product, χ_((1,2)) represents asecond dimensional coordinate (e.g., a y-axis spatial value) for thefirst product, and χ_((1,2)) represents a third dimensional coordinate(e.g., a z-axis spatial value) for the first product. Similarly,χ_((2,1)) represents a first dimensional coordinate for a secondproduct, χ_((2,2)) represents a second dimensional coordinate for thesecond product, and χ_((2,3)) represents a third dimensional coordinatefor the second product. Conceptually, each product may be represented asa point in an n-dimensional space. Continuing with the above-describedexamples of Coke®, Pepsi® and Sprite®, because Coke® and Pepsi® are bothcola products sold in similar markets and potentially have similarpreferences, spatial coordinates for Coke® and Pepsi® are likelyrelatively near each other when compared to Sprite®, which is not a colaproduct. A relative distance between product representations in theexample geometric matrix 600 may be calculated in a manner consistentwith example Equation 9.

$\begin{matrix}{M_{s,v} = {\sum\limits_{d}^{\;}{\left( {\chi_{s,d} - \chi_{v,d}} \right)^{2}.}}} & {{Equation}\mspace{14mu} 9}\end{matrix}$

In the illustrated example of Equation 9, M represents a distancebetween a first item s from the total list of items I, and another itemv, and d represents a dimension from the n dimensions. As describedabove, the example geometric matrix 600 exhibits the least amount offlexibility because it imposes the greatest amount of structure againstthe provided choice data. The estimation performed by the exampleestimator 215 may employ the geometric matrix for circumstances in whichmatrices having greater degrees of freedom result in overfitting. Forinstance, a model (or a matrix within the model) that includesincreasing numbers of parameters becomes more flexible and eventuallyfits the supplied data to the greatest degree, but at the expense ofcomputational loads that may cause estimation inefficiency. Although theexample geometric matrix 600 may not fit the provided choice data aswell as the straight and/or the symmetric matrix, the geometric matrix600 may be appropriate in response to statistically satisfactorymeasures of fit values calculated by the example measure of fit engine216.

In some examples, rigid matrix structures may not fit well with thechoice data that results from the respondent choice modeling exercise.In other words, some product mixes may not follow geometricrelationships, thereby causing the application of the geometric matrixto produce poor statistical measures of fit values. For example,consider a mix of laundry detergent products that includes (a) detergentwith bleach, (b) detergent with color safe bleach and (c) detergent withno bleach. Choice data results may identify a relatively large degree ofsubstitution between (a) and (b) because consumers prefer to have awhites/colors bleach product, and the choice data results may alsoidentify a relatively large degree of substitution between (b) and (c).Continuing with the laundry detergent example, consider that the choicedata results find no substitution between (a) and (c). Generallyspeaking, the geometric matrix adheres to one or more logical axioms toproduce conclusions. As described in the above example, if (a)=(b), and(b)=(c), then geometric principles suggest that (a) should be equal toor similar to (c) from a spatial point of view. However, the examplegeometric model may attempt to force relationships in a mannerinconsistent with the collected choice data and force a similaritybetween (a) and (c) despite choice data suggesting no such relationshipactually occurs. In such circumstances, a poor measure of fit resultsand the example measure of fit engine 216 selects an alternate matrixstructure having a greater degree of flexibility.

In still further examples, subcategories may be employed to, in part,reduce matrix sizes. Generating one or more subcategories imposesfurther constraint on the model and may introduce a degree of analystdiscretion. However, in circumstances where a matrix becomes large dueto a large number of products, employing one or more subcategoriesreduces a computational burden of the model. For example, a matrixrepresenting 100 items includes 100 rows and 100 columns, whichcorresponds to 10,000 individual matrix cells. In the event that 30subcategories are employed, then a number of columns and rows eachcollapse to form a 30 by 30 matrix, thereby substantially reducing acomputational burden of parameter value estimation. For instance, ifPepsi® and Coke® are deemed similar (e.g., any differences between thetwo are inconsequential), then a subcategory indicative of national colabrands may allow the rows and columns associated with Coke® and Pepsi®to collapse together. In other words, multiple products may share thesame M values when they share the same subcategory.

Equation 10 illustrates an example manner in which each model row iscalculated with a weight (w) in view of S subcategories.

$\begin{matrix}{w_{S} = {\frac{\sum\limits_{j \in S}^{\;}^{\beta_{j}}}{\sum\limits_{j}^{\;}^{\beta_{j}}}.}} & {{Equation}\mspace{14mu} 10}\end{matrix}$

In the illustrated example of Equation 10, the numerator notationsignifies to sum over all items in subcategory s. As such, employingsubcategories allows a matrix to be formed as an S by S matrix ratherthan the larger I by I matrix described above. In view of theimplementation of subcategories, choice probability may be calculated ina manner consistent with example Equation 11.

$\begin{matrix}{C_{i} = {\sum\limits_{s}^{\;}{W_{s}{\frac{^{\lbrack{\beta_{i} - M_{s,{vi}} + {{({\beta_{pi} + \beta_{p^{\prime}s}})}\$_{i}}}\rbrack}}{\sum\limits_{j}^{\;}^{\lbrack{\beta_{j} - M_{s,{vj}} + {{({\beta_{pj} + \beta_{p^{\prime}s}})}\$_{j}}}\rbrack}}.}}}} & {{Equation}\mspace{14mu} 11}\end{matrix}$

While an example manner of implementing an example system 100 to modelconsumer choice sourcing has been illustrated in FIGS. 2-6, one or moreof the elements, processes and/or devices illustrated in FIGS. 1-6 maybe combined, divided, re-arranged, omitted, eliminated and/orimplemented in any other way. Further, the example respondent database102, the example product selection database 104, the exampleprice/availability control 106, the example ALS engine 108, the examplechoice modeling engine 202, the example MNL engine 204, the exampleaggregate building engine 206, the example sourcing modifier 208, theexample matrix engine 210, the example matrix symmetry engine 212, theexample matrix spatial engine 214, the example estimator 215, theexample measure of fit engine 216 and/or the example simulation engine218 of FIGS. 1 and 2 may be implemented by hardware, software, firmwareand/or any combination of hardware, software and/or firmware. Thus, forexample, any of the example respondent database 102, the example productselection database 104, the example price/availability control 106, theexample ALS engine 108, the example choice modeling engine 202, theexample MNL engine 204, the example aggregate building engine 206, theexample sourcing modifier 208, the example matrix engine 210, theexample matrix symmetry engine 212, the example matrix spatial engine214, the example estimator 215, the example measure of fit engine 216and/or the example simulation engine 218 of FIGS. 1 and 2 could beimplemented by one or more circuit(s), programmable processsor(s),application specific integrated circuit(s) (ASIC(s)), programmable logicdevice(s) (PLD(s)) and/or field programmable logic device(s) (FPLD(s)),etc. When any of the apparatus claims of the patent are read to cover apurely software and/or firmware implementation, at least one of theexample respondent database 102, the example product selection database104, the example price/availability control 106, the example ALS engine108, the example choice modeling engine 202, the example MNL engine 204,the example aggregate building engine 206, the example sourcing modifier208, the example matrix engine 210, the example matrix symmetry engine212, the example matrix spatial engine 214, the example estimator 215,the example measure of fit engine 216 and/or the example simulationengine 218 of FIGS. 1 and 2 are hereby expressly defined to include atangible computer readable medium such as a memory, DVD, CD, etc.storing the software and/or firmware. Further still, the example system100 of FIG. 1 may include one or more elements, processes and/or devicesin addition to, or instead of, those illustrated in FIGS. 1 and 2,and/or may include more than one of any or all of the illustratedelements, processes and devices.

Flowcharts representative of example machine readable instructions forimplementing the system 100 of FIGS. 1 and 2 are shown in FIGS. 7-9. Inthese examples, the machine readable instructions comprise a program forexecution by a processor such as the processor P105 shown in the examplecomputer P100 discussed below in connection with FIG. 10. The programmay be embodied in software stored on a tangible computer readablemedium such as a CD-ROM, a floppy disk, a hard drive, a digitalversatile disk (DVD), or a memory associated with the processor P105,but the entire program and/or parts thereof could alternatively beexecuted by a device other than the processor P105 and/or embodied infirmware or dedicated hardware. Further, although the example program isdescribed with reference to the flowcharts illustrated in FIGS. 7-9,many other methods of implementing the example system 100 mayalternatively be used. For example, the order of execution of the blocksmay be changed, and/or some of the blocks described may be changed,eliminated, or combined.

As mentioned above, the example processes of FIGS. 7-9 may beimplemented using coded instructions (e.g., computer readableinstructions) stored on a tangible computer readable medium such as ahard disk drive, a flash memory, a read-only memory (ROM), a compactdisk (CD), a digital versatile disk (DVD), a cache, a random-accessmemory (RAM) and/or any other storage media in which information isstored for any duration (e.g., for extended time periods, permanently,brief instances, for temporarily buffering, and/or for caching of theinformation). As used herein, the term tangible computer readable mediumis expressly defined to include any type of computer readable storageand to exclude propagating signals. Additionally or alternatively, theexample processes of FIGS. 7-9 may be implemented using codedinstructions (e.g., computer readable instructions) stored on anon-transitory computer readable medium such as a hard disk drive, aflash memory, a read-only memory, a compact disk, a digital versatiledisk, a cache, a random-access memory and/or any other storage media inwhich information is stored for any duration (e.g., for extended timeperiods, permanently, brief instances, for temporarily buffering, and/orfor caching of the information). As used herein, the term non-transitorycomputer readable medium is expressly defined to include any type ofcomputer readable medium and to exclude propagating signals.

The process 700 of FIG. 7 begins at block 702 where the example choicemodeling engine 202 identifies products of interest to be studied. Theexample choice modeling engine 202 may facilitate a user interface toallow an analyst and/or client select products of interest, which mayinclude existing market products, existing competitive market productsand/or new products that have not yet been offered for sale in themarket. The example product selection database 104 may include one ormore lists of available market products and/or details related to theproducts. In some examples, the product selection database 104 mayinclude data from the product reference library (PRL) cultivated andmanaged by Nielsen®, which codes more than 700,000 items, in which eachitem includes an average of forty (40) descriptive characteristics, isan example source for such product information. However, the examplesystems, methods, apparatus and/or articles of manufacture are notlimited to using the PRL as one or more alternate sources of productreference data may be employed. Product information may include, but isnot limited to product name, manufacturer name, brand, packaging type,product size, flavor, lot number, serial number, nutritional informationand/or a corresponding universal product code (UPC). One or more pricepoints and/or ranges of price points may be identified and associatedwith the identified products of interest to be communicated to one ormore respondents during a choice modeling exercise. Once a set ofproducts of interest are identified, the example choice modeling engineperforms a choice modeling exercise with respondents (block 704) andsaves choice data to the example respondent database 102 (block 706). Asdescribed above, and in further detail below, the stored choice data isutilized during an iterative estimation process to converge parametervalues of an aggregate model generated and/or otherwise built by theexample ALS engine 108 (block 708), such as the example matrix infusedaggregate model structure 500 of FIG. 5. The example aggregate modelgenerated by the ALS engine 108 may be applied in closed-loop format toone or more simulations to calculate choice probability values of one ormore products (block 710).

The program 708 of FIG. 8 illustrates further detail related togenerating the aggregate model described in FIG. 7. In the illustratedexample of FIG. 8, the program 708 invokes the MNL engine 204 toestablish a base MNL model having a number of items equal to those usedin the choice modeling exercise (block 802). For example, if eighty (80)products (items) were selected to be studied, then the example MNLengine 204 generates a MNL model having eighty (80) parameters. Withoutlimitation, the example MNL engine 204 may include product parameters,price parameters and/or any number of parameters that reflect attributepreferences associated with each product.

The example aggregate building engine 206 makes I copies of the base MNLmodel generated by the example MNL engine 204 (block 804). As describedabove, while each MNL model, by itself, exhibits negative effects of theIIA property, the example aggregate building engine 206 builds anaggregate model to, in part, minimize and/or otherwise drown-out thenegative effects of the IIA property. Additionally, to impose a sourcingeffect of every product of interest on every other product of interestin a proportional manner, the example aggregate building engine 206invokes the example sourcing modifier 208 to generate one or more matrixstructures (block 806), as described above and as described in furtherdetail below.

The aggregate model generated by the aggregate building engine 206 andthe matrix generated by the example sourcing modifier 208 areiteratively estimated by the example estimator 215 (block 808). Asdescribed above, the iterative estimations allow the aggregate modelparameters and the matrix parameters to converge to one or more valuesthat fit the choice data stored in the example respondent database 102.Resulting model parameters and matrix parameters are evaluated by theexample measure of fit engine 216 to determine whether the convergedparameter values are statistically appropriate in view of the suppliedchoice data (block 810). If not, then the example measure of fit engine216 invokes the example sourcing modifier 208 to generate an alternatematrix structure having a greater or lesser degree of structure (block812), and the example program 708 returns to block 806. For example, inthe event that a highly structured geometric model fails to convergewith parameters that are statistically appropriate, then a symmetric orstraight matrix may be employed. On the other hand, in the event that astraight matrix becomes computationally intensive and/or suffers fromoverestimation, then the example measure of fit engine may invoke theexample sourcing modifier 208 to generate a matrix having additionalstructure, such as a symmetric matrix or a geometric matrix.

The program 806 of FIG. 9 illustrates further detail related to buildingthe matrix structure described in FIG. 8. In the illustrated example ofFIG. 9, the program 806 determines whether to generate a geometricmatrix (block 902), a straight matrix (block 904) or a symmetric matrix(block 904). In the event a geometric matrix is to be generated (block902), the example sourcing modifier 208 identifies a number of spatialdimensions to use (block 905). Spatial dimensions can be less than orequal to the number of products (items) of interest used in the choicemodeling exercise. A greater number of dimensions (n) result in agreater number of matrix parameters, a greater resolution and a greaterchance for better fitting the supplied choice data. However, a greaternumber of dimensions (n) also results in a greater computational burdenfor the example estimator 215. In some examples, the example sourcingmodifier 208 invokes the matrix spatial engine 214 as a first attemptunder an assumption and/or empirical understanding that a geometricmatrix is an appropriate and efficient choice for the type(s) of productmix of the selected products (I). The Matrix spatial engine 214 buildsthe geometric matrix having n dimensions as columns, and I items as rows(block 906) so that each product pair spatial distance can be calculatedin a manner consistent with example Equation 9 (block 908). Each matrixelement is associated with the matrix infused aggregate model structure,such as the structure 500 of FIG. 5, in a manner that allows the exampleestimator 215 to perform iterative estimations for parameter convergence(block 910).

In the event that a straight matrix is to be employed (block 904), theexample sourcing modifier 208 employs the matrix engine 210 to build asquare matrix of a size based on the number of products (items) ofinterest (I) (block 912). In other words, the example matrix engine 210builds an I×I matrix structure (block 912), and then adds indexparameter placeholders in each matrix cell (block 914). As describedabove, because the matrix row includes a representation of each productof interest (e.g., counting from a matrix row index value of 1 to I),and because the matrix column includes a representation of each productof interest in the same order as those products listed in the row (e.g.,counting from a matrix column index value of 1 to I), then the diagonalcells will each be set to zero. Each matrix element is associated withthe matrix infused aggregate model structure, such as the structure 500of FIG. 5, in a manner that allows the example estimator 215 to performiterative estimations for parameter convergence (block 910).

In the event that a symmetric matrix is to be employed (block 904), thenthe example sourcing modifier 208 employs the matrix symmetry engine 212to build a square matrix of a size based on the number of products(items) of interest (I) (block 916). In other words, the example matrixsymmetry engine 212 builds an IxI matrix structure (block 916), and thenadds index parameter placeholders in each matrix cell (block 918). Toforce a symmetric structure, the example matrix spatial engine 214identifies matching matrix cells on either side of the matrix diagonaland sets them equal to each other (block 920). In some examples, thesymmetric matrix can be implemented as a half-matrix that only employsparameters on the upper or lower half of the matrix diagonal. As such,the symmetric matrix only employs half as many parameters as thestraight matrix during the iterative estimation executed by the exampleestimator 215. Each matrix element is associated with the matrix infusedaggregate model structure, such as the structure 500 of FIG. 5, in amanner that allows the example estimator 215 to perform iterativeestimations for parameter convergence (block 910).

FIG. 10 is a block diagram of an example computer P100 capable ofexecuting the instructions of FIGS. 7, 8 and/or 9 to implement theexample respondent database 102, the example product selection database104, the example price/availability control 106, the example ALS engine108, the example choice modeling engine 202, the example MNL engine 204,the example aggregate building engine 206, the example sourcing modifier208, the example matrix engine 210, the example matrix symmetry engine212, the example matrix spatial engine 214, the example estimator 215,the example measure of fit engine 216 and/or the example simulationengine 218 of FIGS. 1 and 2. The computer P100 can be, for example, aserver, a personal computer, an Internet appliance, or any other type ofcomputing device.

The system P100 of the instant example includes a processor P105. Forexample, the processor P105 can be implemented by one or more Intel®microprocessors from the Pentium® family, the Itanium® family or theXScale® family. Of course, other processors from other families are alsoappropriate.

The processor P105 is in communication with a main memory including avolatile memory P115 and a non-volatile memory P120 via a bus P125. Thevolatile memory P115 may be implemented by Synchronous Dynamic RandomAccess Memory (SDRAM), Dynamic Random Access Memory (DRAM), RAMBUSDynamic Random Access Memory (RDRAM) and/or any other type of randomaccess memory device. The non-volatile memory P120 may be implemented byflash memory and/or any other desired type of memory device. Access tothe main memory P115, P120 is typically controlled by a memorycontroller (not shown).

The computer P100 also includes an interface circuit P130. The interfacecircuit P130 may be implemented by any type of interface standard, suchas an Ethernet interface, a universal serial bus (USB), and/or a PCIexpress interface.

One or more input devices P135 are connected to the interface circuitP130. The input device(s) P135 permit a user to enter data and commandsinto the processor P105. The input device(s) can be implemented by, forexample, a keyboard, a mouse, a touchscreen, a track-pad, a trackball,and/or a voice recognition system.

One or more output devices P140 are also connected to the interfacecircuit P130. The output devices P140 can be implemented, for example,by display devices (e.g., a liquid crystal display, a cathode ray tubedisplay (CRT), and/or other display). The interface circuit P130, thus,typically includes a graphics driver card.

The interface circuit P130 also includes a communication device (notshown) such as a modem or network interface card to facilitate exchangeof data with external computers via a network (e.g., an Ethernetconnection, a digital subscriber line (DSL), a telephone line, coaxialcable, a cellular telephone system, etc.).

The computer P100 also includes one or more mass storage devices P150for storing software and data. Examples of such mass storage devicesP150 include floppy disk drives, hard drive disks, compact disk drivesand digital versatile disk (DVD) drives. The mass storage device P150may implement the example respondent database 102 and/or the exampleproduct selection database 104.

The coded instructions of FIGS. 7-9 may be stored in the mass storagedevice P150, in coded instructions P110 of the volatile memory P115, incoded instructions P112 of the non-volatile memory P120, and/or on aremovable storage medium such as a CD or DVD.

From the foregoing, it will be appreciated that the above disclosedsystems, methods, apparatus and articles of manufacture facilitateprediction of new product performance metrics within one or moregeographies and/or channels of interest when no prior historical salesdata is available for the new product in the corresponding geography orchannel.

Therefore, although certain example methods, apparatus and articles ofmanufacture have been described herein, the scope of coverage of thispatent is not limited thereto. On the contrary, this patent covers allmethods, apparatus and articles of manufacture fairly falling within thescope of the claims either literally or under the doctrine ofequivalents.

What is claimed is:
 1. A computer implemented method to calculate achoice probability, comprising: adding, with a processor, a set ofproducts having respondent choice data to a base multinomial logit (MNL)model, the base MNL model including an item utility parameter and aprice utility parameter associated with corresponding ones of productsin the set of products; generating, with the processor, a number ofcopies of the base MNL model to form an aggregate model based on anumber of the corresponding ones of products in the set of products,each one of the number of copies of the base MNL model exhibiting aneffect of an independence of irrelevant alternatives (IIA) property;proportionally affecting interrelationships, with the processor, betweendissimilar ones of the number of products in the set by insertingsourcing effect values in the aggregate model to be subtracted fromrespective ones of the item utility parameters; estimating, with theprocessor, the item utility parameters of the aggregate model based onthe number of copies of the base MNL model and the respondent choicedata; and calculating, with the processor, the choice probability forthe corresponding ones of the products in the set of products based onthe estimated item utility parameters and the price utility parameters.2. A method as defined in claim 1, wherein inserting the sourcing effectvalues reduces the effect of the IIA property of the aggregate model. 3.A method as defined in claim 1, further comprising converging thesourcing effect values from initially random values via the estimating.4. A method as defined in claim 3, further comprising building aclosed-form choice probability solution based on the converged sourcingeffect values.
 5. A method as defined in claim 1, wherein estimating theitem utility values comprises at least one of performing a maximumlikelihood estimation, performing a Bayes estimation, or performing aminimum squared error estimation.
 6. A method as defined in claim 1,wherein the aggregate model comprises a number of rows equal to thenumber of the corresponding ones of products in the set of products. 7.A method as defined in claim 1, wherein inserting the sourcing effectvalues in the aggregate model to be subtracted from respective ones ofthe item utility parameters generates a product offset value forrespective ones of products in the set of products.
 8. A method asdefined in claim 7, wherein corresponding columns of the number of rowscomprises a product quantity based on a mathematical product of (a) theproduct offset value and (b) a corresponding price utility parameter. 9.A method as defined in claim 8, wherein the corresponding columnsintersect corresponding ones of the number of rows of the aggregatemodel to reflect a relationship between (a) a product of thecorresponding column and (b) a product of the corresponding row.
 10. Anapparatus to calculate a choice probability, comprising: a multinomiallogit (MNL) engine to add a set of products having respondent choicedata to a base MNL model, the MNL engine to include an item utilityparameter and a price utility parameter associated with correspondingones of products in the set of products; an aggregate building engine togenerate a number of copies of the base MNL model to form an aggregatemodel based on a number of the corresponding ones of products in the setof products, each one of the number of copies of the base MNL modelexhibiting an effect of an independence or irrelevant alternatives (IIA)property; a sourcing modifier to proportionally affectinterrelationships between dissimilar ones of the number of products inthe set by inserting sourcing effect values in the aggregate model to besubtracted from respective ones of the item utility parameters; anestimator to estimate the item utility parameters of the aggregate modelbased on the number of copies of the base MNL model and the respondentchoice data; and a simulation engine to calculate the choice probabilityfor the corresponding ones of the products in the set of products basedon the estimated item utility parameters and the price utilityparameters.
 11. An apparatus as defined in claim 10, wherein thesourcing modifier is to reduce the effect of the IIA property of theaggregate model.
 12. An apparatus as defined in claim 10, wherein theestimator is to converge the sourcing effect values from initiallyrandom values.
 13. An apparatus as defined in claim 12, furthercomprising a measure of fit engine to determine a fit value between therespondent choice data and the converged sourcing effect values.
 14. Anapparatus as defined in claim 13, wherein the measure of fit engine isto stop the estimator when a threshold measure of fit value isidentified.
 15. An apparatus as defined in claim 12, wherein theestimator is to build a closed-form choice probability solution based onthe converged sourcing effect values.
 16. An apparatus as defined inclaim 10, wherein the estimator is to use at least one of a maximumlikelihood estimation, a Bayes estimation, or a minimum squared errorestimation.
 17. An apparatus as defined in claim 10, further comprisinga matrix engine to generate a number of rows equal to the number of thecorresponding ones of products in the set of products.
 18. A tangiblemachine-readable storage medium comprising instructions that, whenexecuted, cause a sourcing engine to, at least: add a set of productshaving respondent choice data to a base multinomial logit (MNL) model,the base MNL model including an item utility parameter and a priceutility parameter associated with corresponding ones of products in theset of products; generate a number of copies of the base MNL model toform an aggregate model based on a number of the corresponding ones ofproducts in the set of products, each one of the number of copies of thebase MNL model exhibiting an effect of an independence of irrelevantalternatives (IIA) property; proportionally affect interrelationshipsbetween dissimilar ones of the number of products in the set byinserting sourcing effect values in the aggregate model to be subtractedfrom respective ones of the item utility parameters; estimate the itemutility parameters of the aggregate model based on the number of copiesof the base MNL model and the respondent choice data; and calculate thechoice probability for the corresponding ones of the products in the setof products based on the estimated item utility parameters and the priceutility parameters.
 19. A machine-readable storage medium as defined inclaim 18, further comprising instructions that, when executed, cause thesourcing engine to reduce the effect of the IIA property of theaggregate model in response to inserting the sourcing effect values. 20.A machine-readable storage medium as defined in claim 18, furthercomprising instructions that, when executed, cause the sourcing engineto converge the sourcing effect values from initially random valuesduring the estimation.
 21. A machine-readable storage medium as definedin claim 20, further comprising instructions that, when executed, causethe sourcing engine to build a closed-form choice probability solutionbased on the converged sourcing effect values.
 22. A machine-readablestorage medium as defined in claim 18, further comprising instructionsthat, when executed, cause the sourcing engine to estimate via at leastone of a maximum likelihood estimation, a Bayes estimation, or a minimumsquared error estimation.
 23. A machine-readable storage medium asdefined in claim 18, further comprising instructions that, whenexecuted, cause the sourcing engine to subtract the sourcing effectvalues from respective ones of the item utility parameters to generate aproduct offset value for respective ones of products in the set ofproducts.
 24. A machine-readable storage medium as defined in claim 23,further comprising instructions that, when executed, cause the sourcingengine to calculate a mathematical product of (a) the product offsetvalue and (b) a corresponding price utility parameter.